Question

The following payoff table shows the profit for a decision problem with two states of nature and two decision alternatives:

	State of Nature
Decision Alternative	s1	s2
d1	10	1
d2	4	3

(a)	Suppose P(s1)=0.2 and P(s2)=0.8. What is the best decision using the expected value approach? Round your answer in one decimal place.
	The best decision is decision alternative - Select your answer -d1d2Item 1 , with an expected value of  .
(b)	Perform sensitivity analysis on the payoffs for decision alternative d1. Assume the probabilities are as given in part (a), and find the range of payoffs under states of nature s1 and s2 that will keep the solution found in part (a) optimal. Is the solution more sensitive to the payoff under state of nature s1 or s2? Round your answer in two decimal places.
	The solution is more sensitive to - Select your answer -s1s2Item 3 , as an increment of   for d1(s2) causes a break even between the decision alternatives, whereas it takes an increment of  , to provide the same effect for d1(s1).

Answer 1

P(S₁) = 0.2 ; P(S₂) = 0.8

	State of Nature
Probability of state of Nature	0.2	0.8
Decision Alternative	s1	s2	Expected Value
d1	10	1	2.8
d2	4	3	3.2

A. Using the expected value approach, decision 2 is the best alternative with an expected value of 3.2.

B. Using Goal seek in Excel, we get the following results.

Case 1:

	State of Nature
Probability of state of Nature	0.2	0.8
Decision Alternative	s1	s2	Expected Value
d1	10	1.5	3.2
d2	4	3	3.2

This means that d₁(s₂) has to change from 1 to 1.5 (which is 50%) for the decision to break even.

Case 2:

	State of Nature
Probability of state of Nature	0.2	0.8
Decision Alternative	s1	s2	Expected Value
d1	12	1	3.2
d2	4	3	3.2

Similarly, d₁(s₁) has to change from 10 to 12 (which is 20%) for the decision to break even.

Therefore, solution is more sensitive to d₁(s₁), as a 20% change in d₁(s₁) causes the decision payoff to break even. But , a 50% change in d₁(s₂) will cause the decision payoff to break even.